In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A, B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are automatically bounded. In this paper, we will study linear orthogonality preservers in a unified way. We will show that every surjective linear map between standard operator algebras preserving range/domain orthogonality carries a standard form, and is thus automatically bounded.

In this paper, we give a complete description of the structure of zero product and orthogonality preserving linear maps between W*-algebras. In particular, two W*-algebras are *-isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions. It is also the case when they have equivalent linear and left (right) ideal structures.

Abstract. There are four versions of disjointness structures of a C*-algebra: zero product, range orthogonality, domain orthogonality and doubly orthogonality. Recently, Leung and Wong show that the linear and zero product structures are sufficient to determine the CCR C*-algebras with Hausdorff spectrums. In this paper, we investigate the orthogonality structures of the C*-algebras. More precisely, let θ be a bijective linear map between two C*-algebras with continuous traces. We prove that θ is automatically continuous whenever it preserves range (respectively, domain) orthogonal elements in both senses.Mathematics subject classification (2010): 46J10, 46L05.

Aims. To investigate the applicability of deep learning image assessment software VeriSee DR to different color fundus cameras for the screening of diabetic retinopathy (DR). Methods. Color fundus images of diabetes patients taken with three different nonmydriatic fundus cameras, including 477 Topcon TRC-NW400, 459 Topcon TRC-NW8 series, and 471 Kowa nonmyd 8 series that were judged as “gradable” by one ophthalmologist were enrolled for validation. VeriSee DR was then used for the diagnosis of referable DR according to the International Clinical Diabetic Retinopathy Disease Severity Scale. Gradability, sensitivity, and specificity were calculated for each camera model. Results. All images (100%) from the three camera models were gradable for VeriSee DR. The sensitivity for diagnosing referable DR in the TRC-NW400, TRC-NW8, and non-myd 8 series was 89.3%, 94.6%, and 95.7%, respectively, while the specificity was 94.2%, 90.4%, and 89.3%, respectively. Neither the sensitivity nor the specificity differed significantly between these camera models and the original camera model used for VeriSee DR development ( p = 0.40 , p = 0.065 , respectively). Conclusions. VeriSee DR was applicable to a variety of color fundus cameras with 100% agreement with ophthalmologists in terms of gradability and good sensitivity and specificity for the diagnosis of referable DR.

In this paper, we give a complete description of the structure of separating linear maps between continuous fields of Banach spaces. Some automatic continuity results are obtained.